Subgroups — C₇×#60430 #13237646

Order 1792.

2762 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#577	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₇×#576	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3500	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×C₇×H(5,𝔽₂)	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#3046	C₂	1	3	yes	maximal, complemented
6	C₇×#3045	C₂	1	3	yes	maximal, complemented
7	C₇×#3042	C₂	1	3	yes	maximal, complemented
8	C₇×#3041	C₂	1	3	yes	maximal, complemented
9	C₇×#3040	C₂	1	3	yes	maximal, complemented
10	C₇×#3036	C₂	1	3	yes	maximal, complemented
11	C₇×#3035	C₂	1	3	yes	maximal, complemented
12	C₂×C₇×#463	C₂	1	3	yes	maximal, complemented
13	C₇×#2906	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#2898	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#2897	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₇×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
17	C₂×C₇×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
18	C₂×C₇×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
19	C₇×#577	—	2	8	no	—
20	C₇×#576	—	2	8	no	—
21	C₂×C₇×#137	C₂²	1	3	yes	complemented
22	C₂×C₇×AGL(1,ℤ/8)	C₂²	1	3	yes	—
23	C₂×C₇×AGL(1,ℤ/8)	C₂²	1	3	yes	—
24	C₂×C₇×AGL(1,ℤ/8)	C₂²	1	3	yes	complemented
25	C₂×C₇×#135	C₂²	1	3	yes	—
26	C₂×C₇×#135	C₂²	1	3	yes	complemented
27	C₂²×C₇×SD₁₆	C₂²	1	3	yes	complemented
28	C₂²×C₇×D₈	C₂²	1	3	yes	—
29	C₂×C₇×#131	C₂²	1	1	yes	characteristic
30	C₂×C₇×#131	C₂²	1	1	yes	characteristic
31	C₇×#548	—	2	1	no	—
32	C₇×#548	—	2	1	no	—
33	C₇×#546	—	2	3	no	—
34	C₇×#546	—	2	3	no	—
35	C₇×#536	C₂²	1	3	yes	complemented
36	C₇×#535	C₂²	1	3	yes	complemented
37	C₇×#532	C₂²	1	3	yes	complemented
38	C₂×C₇×#124	C₂²	1	3	yes	complemented
39	C₇×#520	—	2	1	no	—
40	C₇×#520	C₂²	1	1	yes	characteristic
41	C₇×#520	C₂²	1	3	yes	complemented
42	C₇×#518	—	2	3	no	—
43	C₇×#518	C₂²	1	3	yes	complemented
44	C₄×C₇×#41	—	2	1	no	—
45	C₄×C₇×#41	C₂²	1	1	yes	characteristic
46	C₄×C₇×#41	C₂²	1	3	yes	complemented
47	C₂×C₄×C₇×D₄	—	2	3	no	—
48	C₂×C₄×C₇×D₄	C₂²	1	3	yes	complemented
49	C₇×#464	C₂²	1	1	yes	characteristic, complemented
50	C₇×#464	C₂²	1	3	yes	complemented
51	C₇×#464	C₂²	1	6	yes	complemented
52	C₇×#463	C₂²	1	3	yes	complemented
53	C₇×#463	C₂²	1	6	yes	complemented
54	C₇×#463	C₂²	1	6	yes	complemented
55	C₇×#463	C₂²	1	6	yes	complemented
56	C₇×#463	C₂²	1	3	yes	complemented
57	C₇×#463	C₂²	1	6	yes	complemented
58	C₇×#462	C₂²	1	3	yes	complemented
59	C₇×#461	C₂²	1	3	yes	complemented
60	C₇×#461	C₂²	1	6	yes	complemented
61	C₇×#460	C₂²	1	3	yes	complemented
62	C₇×#459	C₂²	1	3	yes	complemented
63	C₇×#459	C₂²	1	6	yes	complemented
64	C₇×#424	C₂²	1	3	yes	complemented
65	C₇×#424	C₂²	1	3	yes	complemented
66	C₇×#423	C₂²	1	3	yes	complemented
67	C₂×C₇×C₄⋊C₈	C₂²	1	3	yes	complemented
68	C₇×#419	C₂²	1	3	yes	complemented
69	C₇×#418	C₂²	1	3	yes	complemented
70	C₇×#417	C₂²	1	3	yes	complemented
71	C₇×#417	C₂²	1	3	yes	complemented
72	C₇×#416	C₂²	1	3	yes	complemented
73	C₇×#416	C₂²	1	3	yes	complemented
74	C₂×C₇×#103	C₂²	1	3	yes	complemented
75	C₂×C₇×#102	C₂²	1	3	yes	complemented
76	#60430	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
77	C₇×2₋¹⁺⁴	—	2	4	no	—
78	C₇×2₋¹⁺⁴	—	2	4	no	—
79	C₇×H(5,𝔽₂)	—	2	4	no	—
80	C₇×H(5,𝔽₂)	—	2	4	no	—
81	C₇×H(5,𝔽₂)	—	2	4	no	—
82	C₇×H(5,𝔽₂)	D₄	1	8	yes	complemented
83	C₂×C₇×#41	—	2	1	no	—
84	C₂×C₇×#41	—	2	1	no	—
85	C₂×C₇×#41	—	2	3	no	—
86	C₂×C₇×#41	C₂³	1	3	yes	—
87	C₂×C₇×#41	C₂³	1	3	yes	—
88	C₂×C₇×#41	C₂³	1	3	yes	—
89	C₂×C₇×#41	C₂³	1	1	yes	characteristic
90	C₂²×C₇×Q₈	—	2	1	no	—
91	C₂²×C₇×Q₈	C₂³	1	3	yes	—
92	C₂²×C₇×D₄	—	2	3	no	—
93	C₂²×C₇×D₄	—	2	3	no	—
94	C₂²×C₇×D₄	C₂³	1	3	yes	—
95	C₂²×C₇×D₄	C₂³	1	3	yes	—
96	C₂³×C₄×C₇	—	2	3	no	—
97	C₇×#137	—	2	12	no	—
98	C₇×AGL(1,ℤ/8)	—	2	12	no	—
99	C₇×AGL(1,ℤ/8)	—	2	12	no	—
100	C₇×AGL(1,ℤ/8)	—	2	12	no	—
101	C₇×#135	—	2	12	no	—
102	C₇×#135	—	2	12	no	—
103	C₂×C₇×Q₁₆	C₂³	1	1	yes	characteristic
104	C₂×C₇×Q₁₆	C₂³	1	3	yes	—
105	C₂×C₇×SD₁₆	—	2	12	no	—
106	C₂×C₇×SD₁₆	C₂³	1	3	yes	—
107	C₂×C₇×SD₁₆	C₂³	1	6	yes	—
108	C₂×C₇×SD₁₆	C₂³	1	3	yes	—
109	C₂×C₇×SD₁₆	C₂³	1	3	yes	—
110	C₂×C₇×SD₁₆	C₂³	1	1	yes	characteristic
111	C₂×C₇×D₈	—	2	12	no	—
112	C₂×C₇×D₈	C₂³	1	3	yes	—
113	C₂×C₇×D₈	C₂³	1	6	yes	—
114	C₂×C₇×D₈	C₂³	1	3	yes	—
115	C₇×#131	—	2	4	no	—
116	C₇×#131	—	2	4	no	—
117	C₂×C₇×M₁₆	C₂³	1	3	yes	—
118	C₂×C₇×M₁₆	C₂³	1	3	yes	—
119	C₂²×C₇×C₈	C₂³	1	3	yes	—
120	C₂²×C₇×C₈	C₂³	1	3	yes	—
121	C₇×C₄⋊Q₈	C₂³	1	3	yes	—
122	C₇×#127	C₂³	1	3	yes	—
123	C₇×#124	—	2	3	no	—
124	C₇×#124	—	2	3	no	—
125	C₇×#124	C₂³	1	3	yes	—
126	C₇×#124	C₂³	1	6	yes	—
127	C₇×#124	C₂³	1	1	yes	characteristic
128	C₇×#123	—	2	6	no	—
129	C₇×C₂²⋊Q₈	—	2	3	no	—
130	C₇×C₂²⋊Q₈	—	2	3	no	—
131	C₇×#121	—	2	3	no	—
132	C₇×#121	—	2	3	no	—
133	C₇×#121	—	2	3	no	—
134	C₇×#121	—	2	3	no	—
135	C₇×#120	—	2	6	no	—
136	C₄×C₇×Q₈	—	2	1	no	—
137	C₄×C₇×Q₈	D₄	1	1	yes	characteristic
138	C₄×C₇×Q₈	D₄	1	1	yes	characteristic
139	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
140	C₄×C₇×Q₈	C₂³	1	3	yes	—
141	C₄×C₇×D₄	—	2	3	no	—
142	C₄×C₇×D₄	—	2	3	no	—
143	C₄×C₇×D₄	—	2	3	no	—
144	C₄×C₇×D₄	—	2	3	no	—
145	C₄×C₇×D₄	—	2	3	no	—
146	C₄×C₇×D₄	—	2	6	no	—
147	C₄×C₇×D₄	—	2	3	no	—
148	C₄×C₇×D₄	—	2	3	no	—
149	C₄×C₇×D₄	—	2	3	no	—
150	C₄×C₇×D₄	—	2	3	no	—
151	C₄×C₇×D₄	D₄	1	3	yes	—
152	C₄×C₇×D₄	D₄	1	3	yes	—
153	C₄×C₇×D₄	C₂³	1	3	yes	—
154	C₄×C₇×D₄	C₂³	1	6	yes	—
155	C₄×C₇×D₄	C₂³	1	3	yes	—
156	C₇×#117	—	2	3	no	—
157	C₇×#117	—	2	3	no	—
158	C₇×#117	C₂³	1	3	yes	—
159	C₇×#117	C₂³	1	3	yes	—
160	C₂×C₇×C₄⋊C₄	—	2	3	no	—
161	C₂×C₇×C₄⋊C₄	C₂³	1	3	yes	—
162	C₂×C₇×C₂²⋊C₄	—	2	3	no	—
163	C₂×C₇×C₂²⋊C₄	—	2	3	no	—
164	C₂×C₇×C₂²⋊C₄	—	2	3	no	—
165	C₂×C₇×C₂²⋊C₄	—	2	6	no	—
166	C₂×C₄²×C₇	—	2	3	no	—
167	C₂×C₄²×C₇	C₂³	1	3	yes	—
168	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
169	C₇×C₄⋊C₈	C₂³	1	3	yes	—
170	C₇×C₄⋊C₈	C₂³	1	3	yes	—
171	C₇×C₄⋊C₈	C₂³	1	3	yes	—
172	C₇×C₄⋊C₈	C₂³	1	6	yes	—
173	C₇×#103	C₂³	1	3	yes	—
174	C₇×#103	C₂³	1	6	yes	—
175	C₇×#103	C₂³	1	1	yes	characteristic
176	C₇×#103	C₂³	1	3	yes	—
177	C₇×#103	C₂³	1	3	yes	—
178	C₇×#102	C₂³	1	3	yes	—
179	C₇×#102	C₂³	1	6	yes	—
180	C₇×#102	C₂³	1	1	yes	characteristic
181	C₇×#102	C₂³	1	3	yes	—
182	C₇×#102	C₂³	1	3	yes	—
183	C₂×#577	C₂×C₇	1	1	yes	characteristic, complemented
184	C₂×#576	C₂×C₇	1	1	yes	characteristic, complemented
185	#3500	C₂×C₇	1	1	yes	characteristic, complemented
186	C₄×H(5,𝔽₂)	C₂×C₇	1	1	yes	characteristic, complemented
187	#3046	C₂×C₇	1	3	yes	complemented
188	#3045	C₂×C₇	1	3	yes	complemented
189	#3042	C₂×C₇	1	3	yes	complemented
190	#3041	C₂×C₇	1	3	yes	complemented
191	#3040	C₂×C₇	1	3	yes	complemented
192	#3036	C₂×C₇	1	3	yes	complemented
193	#3035	C₂×C₇	1	3	yes	complemented
194	C₂×#463	C₂×C₇	1	3	yes	complemented
195	#2906	C₂×C₇	1	1	yes	characteristic, complemented
196	#2898	C₂×C₇	1	1	yes	characteristic, complemented
197	#2897	C₂×C₇	1	1	yes	characteristic, complemented
198	C₂⁴×C₇	—	2	3	no	—
199	C₂⁴×C₇	—	2	3	no	—
200	C₇×#41	—	2	8	no	—
201	C₇×#41	—	2	6	no	—
202	C₇×#41	—	2	6	no	—
203	C₇×#41	—	2	6	no	—
204	C₇×#41	—	2	6	no	—
205	C₇×#41	—	2	6	no	—
206	C₇×#41	—	4	4	no	—
207	C₇×#41	—	4	12	no	—
208	C₇×#41	C₂×D₄	1	12	yes	—
209	C₇×#41	C₂×D₄	1	4	yes	—
210	C₇×#41	#41	1	4	yes	—
211	C₂×C₇×Q₈	—	2	3	no	—
212	C₂×C₇×Q₈	—	2	6	no	—
213	C₂×C₇×Q₈	—	2	6	no	—
214	C₂×C₇×Q₈	—	4	4	no	—
215	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
216	C₂×C₇×Q₈	C₂⁴	1	3	yes	—
217	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
218	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
219	C₂×C₇×D₄	—	2	3	no	—
220	C₂×C₇×D₄	—	2	24	no	—
221	C₂×C₇×D₄	—	2	3	no	—
222	C₂×C₇×D₄	—	2	3	no	—
223	C₂×C₇×D₄	—	2	3	no	—
224	C₂×C₇×D₄	—	2	6	no	—
225	C₂×C₇×D₄	—	2	3	no	—
226	C₂×C₇×D₄	—	2	3	no	—
227	C₂×C₇×D₄	—	2	3	no	—
228	C₂×C₇×D₄	—	2	6	no	—
229	C₂×C₇×D₄	—	2	6	no	—
230	C₂×C₇×D₄	—	4	12	no	—
231	C₂×C₇×D₄	C₂×D₄	1	12	yes	—
232	C₂×C₇×D₄	C₂×D₄	1	3	yes	—
233	C₂×C₇×D₄	C₂⁴	1	3	yes	—
234	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
235	C₂×C₇×D₄	C₂⁴	1	3	yes	—
236	C₂²×C₄×C₇	—	2	3	no	—
237	C₂²×C₄×C₇	—	2	3	no	—
238	C₂²×C₄×C₇	—	2	3	no	—
239	C₂²×C₄×C₇	—	2	3	no	—
240	C₂²×C₄×C₇	—	2	3	no	—
241	C₂²×C₄×C₇	—	2	3	no	—
242	C₂²×C₄×C₇	—	2	3	no	—
243	C₂²×C₄×C₇	—	2	6	no	—
244	C₂²×C₄×C₇	—	8	6	no	—
245	C₂²×C₄×C₇	C₂×D₄	1	3	yes	—
246	C₂²×C₄×C₇	C₂×D₄	1	3	yes	—
247	C₂²×C₄×C₇	C₂⁴	1	3	yes	—
248	C₇×Q₁₆	—	2	2	no	—
249	C₇×Q₁₆	—	2	6	no	—
250	C₇×SD₁₆	—	2	2	no	—
251	C₇×SD₁₆	—	2	6	no	—
252	C₇×SD₁₆	—	2	6	no	—
253	C₇×SD₁₆	—	2	12	no	—
254	C₇×SD₁₆	—	2	6	no	—
255	C₇×D₈	—	2	6	no	—
256	C₇×D₈	—	2	12	no	—
257	C₇×D₈	—	2	6	no	—
258	C₇×M₁₆	—	2	6	no	—
259	C₇×M₁₆	—	2	6	no	—
260	C₂×C₇×C₈	—	2	6	no	—
261	C₂×C₇×C₈	—	2	6	no	—
262	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
263	C₂×C₇×C₈	C₂⁴	1	3	yes	—
264	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
265	C₂×C₇×C₈	C₂⁴	1	3	yes	—
266	C₇×C₄⋊C₄	—	2	3	no	—
267	C₇×C₄⋊C₄	—	2	3	no	—
268	C₇×C₄⋊C₄	—	2	1	no	—
269	C₇×C₄⋊C₄	—	2	3	no	—
270	C₇×C₄⋊C₄	—	2	3	no	—
271	C₇×C₄⋊C₄	C₂×D₄	1	3	yes	—
272	C₇×C₄⋊C₄	C₂×D₄	1	3	yes	—
273	C₇×C₄⋊C₄	C₂⁴	1	3	yes	—
274	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
275	C₇×C₂²⋊C₄	—	2	3	no	—
276	C₇×C₂²⋊C₄	—	2	3	no	—
277	C₇×C₂²⋊C₄	—	2	6	no	—
278	C₇×C₂²⋊C₄	—	2	3	no	—
279	C₇×C₂²⋊C₄	—	2	3	no	—
280	C₇×C₂²⋊C₄	—	2	3	no	—
281	C₇×C₂²⋊C₄	—	2	6	no	—
282	C₇×C₂²⋊C₄	—	2	6	no	—
283	C₇×C₂²⋊C₄	—	2	1	no	—
284	C₇×C₂²⋊C₄	—	2	1	no	—
285	C₇×C₂²⋊C₄	C₂×D₄	1	6	yes	—
286	C₄²×C₇	—	2	1	no	—
287	C₄²×C₇	—	2	3	no	—
288	C₄²×C₇	—	2	3	no	—
289	C₄²×C₇	C₂×D₄	1	3	yes	—
290	C₄²×C₇	C₂×D₄	1	3	yes	—
291	C₄²×C₇	C₂⁴	1	1	yes	characteristic
292	C₄²×C₇	C₂⁴	1	3	yes	—
293	C₂×2₋¹⁺⁴	C₂²×C₇	1	1	yes	characteristic
294	C₂×H(5,𝔽₂)	C₂²×C₇	1	1	yes	characteristic
295	C₂×H(5,𝔽₂)	C₂²×C₇	1	1	yes	characteristic
296	#577	—	2	8	no	—
297	#576	—	2	8	no	—
298	C₂×#137	C₂²×C₇	1	3	yes	complemented
299	C₂×AGL(1,ℤ/8)	C₂²×C₇	1	3	yes	—
300	C₂×AGL(1,ℤ/8)	C₂²×C₇	1	3	yes	—
301	C₂×AGL(1,ℤ/8)	C₂²×C₇	1	3	yes	complemented
302	C₂×#135	C₂²×C₇	1	3	yes	—
303	C₂×#135	C₂²×C₇	1	3	yes	complemented
304	C₂²×SD₁₆	C₂²×C₇	1	3	yes	complemented
305	C₂²×D₈	C₂²×C₇	1	3	yes	—
306	C₂×#131	C₂²×C₇	1	1	yes	characteristic
307	C₂×#131	C₂²×C₇	1	1	yes	characteristic
308	#548	—	2	1	no	—
309	#548	—	2	1	no	—
310	#546	—	2	3	no	—
311	#546	—	2	3	no	—
312	#536	C₂²×C₇	1	3	yes	complemented
313	#535	C₂²×C₇	1	3	yes	complemented
314	#532	C₂²×C₇	1	3	yes	complemented
315	C₂×#124	C₂²×C₇	1	3	yes	complemented
316	#520	—	2	1	no	—
317	#520	C₂²×C₇	1	1	yes	characteristic
318	#520	C₂²×C₇	1	3	yes	complemented
319	#518	—	2	3	no	—
320	#518	C₂²×C₇	1	3	yes	complemented
321	C₄×#41	—	2	1	no	—
322	C₄×#41	C₂²×C₇	1	1	yes	characteristic
323	C₄×#41	C₂²×C₇	1	3	yes	complemented
324	C₂×C₄×D₄	—	2	3	no	—
325	C₂×C₄×D₄	C₂²×C₇	1	3	yes	complemented
326	#464	C₂²×C₇	1	1	yes	characteristic, complemented
327	#464	C₂²×C₇	1	3	yes	complemented
328	#464	C₂²×C₇	1	6	yes	complemented
329	#463	C₂²×C₇	1	3	yes	complemented
330	#463	C₂²×C₇	1	6	yes	complemented
331	#463	C₂²×C₇	1	6	yes	complemented
332	#463	C₂²×C₇	1	6	yes	complemented
333	#463	C₂²×C₇	1	3	yes	complemented
334	#463	C₂²×C₇	1	6	yes	complemented
335	#462	C₂²×C₇	1	3	yes	complemented
336	#461	C₂²×C₇	1	3	yes	complemented
337	#461	C₂²×C₇	1	6	yes	complemented
338	#460	C₂²×C₇	1	3	yes	complemented
339	#459	C₂²×C₇	1	3	yes	complemented
340	#459	C₂²×C₇	1	6	yes	complemented
341	#424	C₂²×C₇	1	3	yes	complemented
342	#424	C₂²×C₇	1	3	yes	complemented
343	#423	C₂²×C₇	1	3	yes	complemented
344	C₂×C₄⋊C₈	C₂²×C₇	1	3	yes	complemented
345	#419	C₂²×C₇	1	3	yes	complemented
346	#418	C₂²×C₇	1	3	yes	complemented
347	#417	C₂²×C₇	1	3	yes	complemented
348	#417	C₂²×C₇	1	3	yes	complemented
349	#416	C₂²×C₇	1	3	yes	complemented
350	#416	C₂²×C₇	1	3	yes	complemented
351	C₂×#103	C₂²×C₇	1	3	yes	complemented
352	C₂×#102	C₂²×C₇	1	3	yes	complemented
353	C₂³×C₇	—	2	3	no	—
354	C₂³×C₇	—	2	12	no	—
355	C₂³×C₇	—	2	3	no	—
356	C₂³×C₇	—	2	1	no	—
357	C₂³×C₇	—	4	6	no	—
358	C₂³×C₇	—	8	3	no	—
359	C₂³×C₇	—	8	3	no	—
360	C₂³×C₇	—	8	3	no	—
361	C₂³×C₇	—	8	3	no	—
362	C₂³×C₇	C₂²×D₄	1	3	yes	—
363	C₇×Q₈	—	2	1	no	—
364	C₇×Q₈	—	2	3	no	—
365	C₇×Q₈	—	2	1	no	—
366	C₇×Q₈	—	2	3	no	—
367	C₇×Q₈	—	2	1	no	—
368	C₇×Q₈	—	4	6	no	—
369	C₇×Q₈	#121	1	4	yes	—
370	C₇×Q₈	C₂²×D₄	1	2	yes	—
371	C₇×D₄	—	2	12	no	—
372	C₇×D₄	—	2	12	no	—
373	C₇×D₄	—	2	3	no	—
374	C₇×D₄	—	2	1	no	—
375	C₇×D₄	—	2	3	no	—
376	C₇×D₄	—	2	3	no	—
377	C₇×D₄	—	2	1	no	—
378	C₇×D₄	—	4	6	no	—
379	C₇×D₄	—	4	6	no	—
380	C₇×D₄	—	4	6	no	—
381	C₇×D₄	—	8	3	no	—
382	C₇×D₄	—	8	3	no	—
383	C₇×D₄	#121	1	12	yes	—
384	C₇×D₄	C₂²×D₄	1	6	yes	—
385	C₂×C₄×C₇	—	2	1	no	—
386	C₂×C₄×C₇	—	2	12	no	—
387	C₂×C₄×C₇	—	2	1	no	—
388	C₂×C₄×C₇	—	2	3	no	—
389	C₂×C₄×C₇	—	2	3	no	—
390	C₂×C₄×C₇	—	2	1	no	—
391	C₂×C₄×C₇	—	4	3	no	—
392	C₂×C₄×C₇	—	4	3	no	—
393	C₂×C₄×C₇	—	4	6	no	—
394	C₂×C₄×C₇	—	4	6	no	—
395	C₂×C₄×C₇	—	4	6	no	—
396	C₂×C₄×C₇	—	4	6	no	—
397	C₂×C₄×C₇	—	8	3	no	—
398	C₂×C₄×C₇	—	8	6	no	—
399	C₂×C₄×C₇	—	8	3	no	—
400	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
401	C₂×C₄×C₇	C₂²×D₄	1	3	yes	—
402	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
403	C₂×C₄×C₇	C₂²×D₄	1	3	yes	—
404	C₂×C₄×C₇	C₂²×D₄	1	3	yes	—
405	C₂×C₄×C₇	C₂²×D₄	1	6	yes	—
406	C₂×C₄×C₇	C₂×#41	1	6	yes	—
407	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
408	C₇×C₈	—	2	1	no	—
409	C₇×C₈	—	2	1	no	—
410	C₇×C₈	—	2	3	no	—
411	C₇×C₈	—	2	3	no	—
412	2₋¹⁺⁴	—	2	4	no	—
413	2₋¹⁺⁴	—	2	4	no	—
414	H(5,𝔽₂)	—	2	4	no	—
415	H(5,𝔽₂)	—	2	4	no	—
416	H(5,𝔽₂)	—	2	4	no	—
417	H(5,𝔽₂)	C₇×D₄	1	8	yes	complemented
418	C₂×#41	—	2	1	no	—
419	C₂×#41	—	2	1	no	—
420	C₂×#41	—	2	3	no	—
421	C₂×#41	C₂³×C₇	1	3	yes	—
422	C₂×#41	C₂³×C₇	1	3	yes	—
423	C₂×#41	C₂³×C₇	1	3	yes	—
424	C₂×#41	C₂³×C₇	1	1	yes	characteristic
425	C₂²×Q₈	—	2	1	no	—
426	C₂²×Q₈	C₂³×C₇	1	3	yes	—
427	C₂²×D₄	—	2	3	no	—
428	C₂²×D₄	—	2	3	no	—
429	C₂²×D₄	C₂³×C₇	1	3	yes	—
430	C₂²×D₄	C₂³×C₇	1	3	yes	—
431	C₂³×C₄	—	2	3	no	—
432	#137	—	2	12	no	—
433	AGL(1,ℤ/8)	—	2	12	no	—
434	AGL(1,ℤ/8)	—	2	12	no	—
435	AGL(1,ℤ/8)	—	2	12	no	—
436	#135	—	2	12	no	—
437	#135	—	2	12	no	—
438	C₂×Q₁₆	C₂³×C₇	1	1	yes	characteristic
439	C₂×Q₁₆	C₂³×C₇	1	3	yes	—
440	C₂×SD₁₆	—	2	12	no	—
441	C₂×SD₁₆	C₂³×C₇	1	3	yes	—
442	C₂×SD₁₆	C₂³×C₇	1	6	yes	—
443	C₂×SD₁₆	C₂³×C₇	1	3	yes	—
444	C₂×SD₁₆	C₂³×C₇	1	3	yes	—
445	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
446	C₂×D₈	—	2	12	no	—
447	C₂×D₈	C₂³×C₇	1	3	yes	—
448	C₂×D₈	C₂³×C₇	1	6	yes	—
449	C₂×D₈	C₂³×C₇	1	3	yes	—
450	#131	—	2	4	no	—
451	#131	—	2	4	no	—
452	C₂×M₁₆	C₂³×C₇	1	3	yes	—
453	C₂×M₁₆	C₂³×C₇	1	3	yes	—
454	C₂²×C₈	C₂³×C₇	1	3	yes	—
455	C₂²×C₈	C₂³×C₇	1	3	yes	—
456	C₄⋊Q₈	C₂³×C₇	1	3	yes	—
457	#127	C₂³×C₇	1	3	yes	—
458	#124	—	2	3	no	—
459	#124	—	2	3	no	—
460	#124	C₂³×C₇	1	3	yes	—
461	#124	C₂³×C₇	1	6	yes	—
462	#124	C₂³×C₇	1	1	yes	characteristic
463	#123	—	2	6	no	—
464	C₂²⋊Q₈	—	2	3	no	—
465	C₂²⋊Q₈	—	2	3	no	—
466	#121	—	2	3	no	—
467	#121	—	2	3	no	—
468	#121	—	2	3	no	—
469	#121	—	2	3	no	—
470	#120	—	2	6	no	—
471	C₄×Q₈	—	2	1	no	—
472	C₄×Q₈	C₇×D₄	1	1	yes	characteristic
473	C₄×Q₈	C₇×D₄	1	1	yes	characteristic
474	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
475	C₄×Q₈	C₂³×C₇	1	3	yes	—
476	C₄×D₄	—	2	3	no	—
477	C₄×D₄	—	2	3	no	—
478	C₄×D₄	—	2	3	no	—
479	C₄×D₄	—	2	3	no	—
480	C₄×D₄	—	2	3	no	—
481	C₄×D₄	—	2	6	no	—
482	C₄×D₄	—	2	3	no	—
483	C₄×D₄	—	2	3	no	—
484	C₄×D₄	—	2	3	no	—
485	C₄×D₄	—	2	3	no	—
486	C₄×D₄	C₇×D₄	1	3	yes	—
487	C₄×D₄	C₇×D₄	1	3	yes	—
488	C₄×D₄	C₂³×C₇	1	3	yes	—
489	C₄×D₄	C₂³×C₇	1	6	yes	—
490	C₄×D₄	C₂³×C₇	1	3	yes	—
491	#117	—	2	3	no	—
492	#117	—	2	3	no	—
493	#117	C₂³×C₇	1	3	yes	—
494	#117	C₂³×C₇	1	3	yes	—
495	C₂×C₄⋊C₄	—	2	3	no	—
496	C₂×C₄⋊C₄	C₂³×C₇	1	3	yes	—
497	C₂×C₂²⋊C₄	—	2	3	no	—
498	C₂×C₂²⋊C₄	—	2	3	no	—
499	C₂×C₂²⋊C₄	—	2	3	no	—
500	C₂×C₂²⋊C₄	—	2	6	no	—
501	C₂×C₄²	—	2	3	no	—
502	C₂×C₄²	C₂³×C₇	1	3	yes	—
503	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
504	C₄⋊C₈	C₂³×C₇	1	3	yes	—
505	C₄⋊C₈	C₂³×C₇	1	3	yes	—
506	C₄⋊C₈	C₂³×C₇	1	3	yes	—
507	C₄⋊C₈	C₂³×C₇	1	6	yes	—
508	#103	C₂³×C₇	1	3	yes	—
509	#103	C₂³×C₇	1	6	yes	—
510	#103	C₂³×C₇	1	1	yes	characteristic
511	#103	C₂³×C₇	1	3	yes	—
512	#103	C₂³×C₇	1	3	yes	—
513	#102	C₂³×C₇	1	3	yes	—
514	#102	C₂³×C₇	1	6	yes	—
515	#102	C₂³×C₇	1	1	yes	characteristic
516	#102	C₂³×C₇	1	3	yes	—
517	#102	C₂³×C₇	1	3	yes	—
518	C₂²×C₇	—	2	3	no	—
519	C₂²×C₇	—	2	3	no	—
520	C₂²×C₇	—	2	6	no	—
521	C₂²×C₇	—	4	3	no	—
522	C₂²×C₇	—	4	3	no	—
523	C₂²×C₇	—	4	1	no	—
524	C₂²×C₇	—	4	3	no	—
525	C₂²×C₇	—	4	1	no	—
526	C₂²×C₇	—	4	3	no	—
527	C₂²×C₇	—	4	1	no	—
528	C₂²×C₇	—	4	3	no	—
529	C₂²×C₇	—	8	12	no	—
530	C₂²×C₇	—	16	6	no	—
531	C₂²×C₇	C₂×#121	1	6	yes	—
532	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
533	C₄×C₇	—	2	1	no	—
534	C₄×C₇	—	2	3	no	—
535	C₄×C₇	—	2	1	no	—
536	C₄×C₇	—	2	3	no	—
537	C₄×C₇	—	2	2	no	—
538	C₄×C₇	—	4	1	no	—
539	C₄×C₇	—	4	3	no	—
540	C₄×C₇	—	4	1	no	—
541	C₄×C₇	—	4	3	no	—
542	C₄×C₇	C₂×#121	1	6	yes	—
543	C₄×C₇	C₂³×D₄	1	1	yes	characteristic
544	C₄×C₇	C₂²×#41	1	1	yes	characteristic
545	C₂⁴	—	2	3	no	—
546	C₂⁴	—	2	3	no	—
547	#41	—	2	8	no	—
548	#41	—	2	6	no	—
549	#41	—	2	6	no	—
550	#41	—	2	6	no	—
551	#41	—	2	6	no	—
552	#41	—	2	6	no	—
553	#41	—	4	4	no	—
554	#41	—	4	12	no	—
555	#41	C₂×C₇×D₄	1	12	yes	—
556	#41	C₂×C₇×D₄	1	4	yes	—
557	#41	C₇×#41	1	4	yes	—
558	C₂×Q₈	—	2	3	no	—
559	C₂×Q₈	—	2	6	no	—
560	C₂×Q₈	—	2	6	no	—
561	C₂×Q₈	—	4	4	no	—
562	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
563	C₂×Q₈	C₂⁴×C₇	1	3	yes	—
564	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
565	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
566	C₂×D₄	—	2	3	no	—
567	C₂×D₄	—	2	24	no	—
568	C₂×D₄	—	2	3	no	—
569	C₂×D₄	—	2	3	no	—
570	C₂×D₄	—	2	3	no	—
571	C₂×D₄	—	2	6	no	—
572	C₂×D₄	—	2	3	no	—
573	C₂×D₄	—	2	3	no	—
574	C₂×D₄	—	2	3	no	—
575	C₂×D₄	—	2	6	no	—
576	C₂×D₄	—	2	6	no	—
577	C₂×D₄	—	4	12	no	—
578	C₂×D₄	C₂×C₇×D₄	1	12	yes	—
579	C₂×D₄	C₂×C₇×D₄	1	3	yes	—
580	C₂×D₄	C₂⁴×C₇	1	3	yes	—
581	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
582	C₂×D₄	C₂⁴×C₇	1	3	yes	—
583	C₂²×C₄	—	2	3	no	—
584	C₂²×C₄	—	2	3	no	—
585	C₂²×C₄	—	2	3	no	—
586	C₂²×C₄	—	2	3	no	—
587	C₂²×C₄	—	2	3	no	—
588	C₂²×C₄	—	2	3	no	—
589	C₂²×C₄	—	2	3	no	—
590	C₂²×C₄	—	2	6	no	—
591	C₂²×C₄	—	8	6	no	—
592	C₂²×C₄	C₂×C₇×D₄	1	3	yes	—
593	C₂²×C₄	C₂×C₇×D₄	1	3	yes	—
594	C₂²×C₄	C₂⁴×C₇	1	3	yes	—
595	Q₁₆	—	2	2	no	—
596	Q₁₆	—	2	6	no	—
597	SD₁₆	—	2	2	no	—
598	SD₁₆	—	2	6	no	—
599	SD₁₆	—	2	6	no	—
600	SD₁₆	—	2	12	no	—
601	SD₁₆	—	2	6	no	—
602	D₈	—	2	6	no	—
603	D₈	—	2	12	no	—
604	D₈	—	2	6	no	—
605	M₁₆	—	2	6	no	—
606	M₁₆	—	2	6	no	—
607	C₂×C₈	—	2	6	no	—
608	C₂×C₈	—	2	6	no	—
609	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
610	C₂×C₈	C₂⁴×C₇	1	3	yes	—
611	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
612	C₂×C₈	C₂⁴×C₇	1	3	yes	—
613	C₄⋊C₄	—	2	3	no	—
614	C₄⋊C₄	—	2	3	no	—
615	C₄⋊C₄	—	2	1	no	—
616	C₄⋊C₄	—	2	3	no	—
617	C₄⋊C₄	—	2	3	no	—
618	C₄⋊C₄	C₂×C₇×D₄	1	3	yes	—
619	C₄⋊C₄	C₂×C₇×D₄	1	3	yes	—
620	C₄⋊C₄	C₂⁴×C₇	1	3	yes	—
621	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
622	C₂²⋊C₄	—	2	3	no	—
623	C₂²⋊C₄	—	2	3	no	—
624	C₂²⋊C₄	—	2	6	no	—
625	C₂²⋊C₄	—	2	3	no	—
626	C₂²⋊C₄	—	2	3	no	—
627	C₂²⋊C₄	—	2	3	no	—
628	C₂²⋊C₄	—	2	6	no	—
629	C₂²⋊C₄	—	2	6	no	—
630	C₂²⋊C₄	—	2	1	no	—
631	C₂²⋊C₄	—	2	1	no	—
632	C₂²⋊C₄	C₂×C₇×D₄	1	6	yes	—
633	C₄²	—	2	1	no	—
634	C₄²	—	2	3	no	—
635	C₄²	—	2	3	no	—
636	C₄²	C₂×C₇×D₄	1	3	yes	—
637	C₄²	C₂×C₇×D₄	1	3	yes	—
638	C₄²	C₂⁴×C₇	1	1	yes	characteristic
639	C₄²	C₂⁴×C₇	1	3	yes	—
640	C₂×C₇	—	2	6	no	—
641	C₂×C₇	—	4	6	no	—
642	C₂×C₇	—	8	1	no	—
643	C₂×C₇	—	8	3	no	—
644	C₂×C₇	C₂²×#121	1	1	yes	characteristic
645	C₂×C₇	#3584	1	1	yes	characteristic
646	C₂×C₇	#3585	1	1	yes	characteristic
647	C₂³	—	2	3	no	—
648	C₂³	—	2	12	no	—
649	C₂³	—	2	3	no	—
650	C₂³	—	2	1	no	—
651	C₂³	—	4	6	no	—
652	C₂³	—	8	3	no	—
653	C₂³	—	8	3	no	—
654	C₂³	—	8	3	no	—
655	C₂³	—	8	3	no	—
656	C₂³	C₂²×C₇×D₄	1	3	yes	—
657	Q₈	—	2	1	no	—
658	Q₈	—	2	3	no	—
659	Q₈	—	2	1	no	—
660	Q₈	—	2	3	no	—
661	Q₈	—	2	1	no	—
662	Q₈	—	4	6	no	—
663	Q₈	C₇×#121	1	4	yes	—
664	Q₈	C₂²×C₇×D₄	1	2	yes	—
665	D₄	—	2	12	no	—
666	D₄	—	2	3	no	—
667	D₄	—	2	1	no	—
668	D₄	—	2	3	no	—
669	D₄	—	2	3	no	—
670	D₄	—	2	1	no	—
671	D₄	—	2	12	no	—
672	D₄	—	4	6	no	—
673	D₄	—	4	6	no	—
674	D₄	—	4	6	no	—
675	D₄	—	8	3	no	—
676	D₄	—	8	3	no	—
677	D₄	C₇×#121	1	12	yes	—
678	D₄	C₂²×C₇×D₄	1	6	yes	—
679	C₂×C₄	—	2	1	no	—
680	C₂×C₄	—	2	12	no	—
681	C₂×C₄	—	2	1	no	—
682	C₂×C₄	—	2	3	no	—
683	C₂×C₄	—	2	3	no	—
684	C₂×C₄	—	2	1	no	—
685	C₂×C₄	—	4	3	no	—
686	C₂×C₄	—	4	3	no	—
687	C₂×C₄	—	4	6	no	—
688	C₂×C₄	—	4	6	no	—
689	C₂×C₄	—	4	6	no	—
690	C₂×C₄	—	4	6	no	—
691	C₂×C₄	—	8	3	no	—
692	C₂×C₄	—	8	6	no	—
693	C₂×C₄	—	8	3	no	—
694	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
695	C₂×C₄	C₂²×C₇×D₄	1	3	yes	—
696	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
697	C₂×C₄	C₂²×C₇×D₄	1	3	yes	—
698	C₂×C₄	C₂²×C₇×D₄	1	6	yes	—
699	C₂×C₄	C₂²×C₇×D₄	1	3	yes	—
700	C₂×C₄	C₂×C₇×#41	1	6	yes	—
701	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
702	C₈	—	2	1	no	—
703	C₈	—	2	1	no	—
704	C₈	—	2	3	no	—
705	C₈	—	2	3	no	—
706	C₇	#60430	1	1	yes	characteristic, direct product factor, Sylow
707	C₂²	—	2	3	no	—
708	C₂²	—	2	3	no	—
709	C₂²	—	2	6	no	—
710	C₂²	—	4	3	no	—
711	C₂²	—	4	3	no	—
712	C₂²	—	4	1	no	—
713	C₂²	—	4	3	no	—
714	C₂²	—	4	1	no	—
715	C₂²	—	4	3	no	—
716	C₂²	—	4	1	no	—
717	C₂²	—	4	3	no	—
718	C₂²	—	8	12	no	—
719	C₂²	—	16	6	no	—
720	C₂²	C₂×C₇×#121	1	6	yes	—
721	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
722	C₄	—	2	1	no	—
723	C₄	—	2	3	no	—
724	C₄	—	2	1	no	—
725	C₄	—	2	3	no	—
726	C₄	—	2	2	no	—
727	C₄	—	4	1	no	—
728	C₄	—	4	3	no	—
729	C₄	—	4	1	no	—
730	C₄	—	4	3	no	—
731	C₄	C₂×C₇×#121	1	6	yes	—
732	C₄	C₂³×C₇×D₄	1	1	yes	characteristic
733	C₄	C₂²×C₇×#41	1	1	yes	characteristic
734	C₂	—	2	6	no	—
735	C₂	—	4	6	no	—
736	C₂	—	8	3	no	—
737	C₂	—	8	1	no	—
738	C₂	C₂²×C₇×#121	1	1	yes	characteristic
739	C₂	C₇×#3584	1	1	yes	characteristic
740	C₂	C₇×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₄×C₇×#41 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×C₇×#577	C₂	semidirect
2. C₂×C₇×#576	C₂	semidirect
3. C₇×#3500	C₂	semidirect
4. C₄×C₇×H(5,𝔽₂)	C₂	semidirect
5. C₇×#3046	C₂	semidirect
6. C₇×#3045	C₂	semidirect
7. C₇×#3042	C₂	semidirect
8. C₇×#3041	C₂	semidirect
9. C₇×#3040	C₂	semidirect
10. C₇×#3036	C₂	semidirect
11. C₇×#3035	C₂	semidirect
12. C₂×C₇×#463	C₂	semidirect
13. C₇×#2906	C₂	semidirect
14. C₇×#2898	C₂	semidirect
15. C₇×#2897	C₂	semidirect
21. C₂×C₇×#137	C₂²	semidirect
24. C₂×C₇×AGL(1,ℤ/8)	C₂²	semidirect
26. C₂×C₇×#135	C₂²	semidirect
27. C₂²×C₇×SD₁₆	C₂²	semidirect
35. C₇×#536	C₂²	semidirect
36. C₇×#535	C₂²	semidirect
37. C₇×#532	C₂²	semidirect
38. C₂×C₇×#124	C₂²	semidirect
41. C₇×#520	C₂²	semidirect
43. C₇×#518	C₂²	semidirect
46. C₄×C₇×#41	C₂²	semidirect
48. C₂×C₄×C₇×D₄	C₂²	semidirect
49. C₇×#464	C₂²	semidirect
50. C₇×#464	C₂²	semidirect
51. C₇×#464	C₂²	semidirect
52. C₇×#463	C₂²	semidirect
53. C₇×#463	C₂²	semidirect
54. C₇×#463	C₂²	semidirect
55. C₇×#463	C₂²	semidirect
56. C₇×#463	C₂²	semidirect
57. C₇×#463	C₂²	semidirect
58. C₇×#462	C₂²	semidirect
59. C₇×#461	C₂²	semidirect
60. C₇×#461	C₂²	semidirect
61. C₇×#460	C₂²	semidirect
62. C₇×#459	C₂²	semidirect
63. C₇×#459	C₂²	semidirect
64. C₇×#424	C₂²	semidirect
65. C₇×#424	C₂²	semidirect
66. C₇×#423	C₂²	semidirect
67. C₂×C₇×C₄⋊C₈	C₂²	semidirect
68. C₇×#419	C₂²	semidirect
69. C₇×#418	C₂²	semidirect
70. C₇×#417	C₂²	semidirect
71. C₇×#417	C₂²	semidirect
72. C₇×#416	C₂²	semidirect
73. C₇×#416	C₂²	semidirect
74. C₂×C₇×#103	C₂²	semidirect
75. C₂×C₇×#102	C₂²	semidirect
76. #60430	C₇	direct (N × H)
82. C₇×H(5,𝔽₂)	D₄	semidirect
183. C₂×#577	C₂×C₇	semidirect
184. C₂×#576	C₂×C₇	semidirect
185. #3500	C₂×C₇	semidirect
186. C₄×H(5,𝔽₂)	C₂×C₇	semidirect
187. #3046	C₂×C₇	semidirect
188. #3045	C₂×C₇	semidirect
189. #3042	C₂×C₇	semidirect
190. #3041	C₂×C₇	semidirect
191. #3040	C₂×C₇	semidirect
192. #3036	C₂×C₇	semidirect
193. #3035	C₂×C₇	semidirect
194. C₂×#463	C₂×C₇	semidirect
195. #2906	C₂×C₇	semidirect
196. #2898	C₂×C₇	semidirect
197. #2897	C₂×C₇	semidirect
298. C₂×#137	C₂²×C₇	semidirect
301. C₂×AGL(1,ℤ/8)	C₂²×C₇	semidirect
303. C₂×#135	C₂²×C₇	semidirect
304. C₂²×SD₁₆	C₂²×C₇	semidirect
312. #536	C₂²×C₇	semidirect
313. #535	C₂²×C₇	semidirect
314. #532	C₂²×C₇	semidirect
315. C₂×#124	C₂²×C₇	semidirect
318. #520	C₂²×C₇	semidirect
320. #518	C₂²×C₇	semidirect
323. C₄×#41	C₂²×C₇	semidirect
325. C₂×C₄×D₄	C₂²×C₇	semidirect
326. #464	C₂²×C₇	semidirect
327. #464	C₂²×C₇	semidirect
328. #464	C₂²×C₇	semidirect
329. #463	C₂²×C₇	semidirect
330. #463	C₂²×C₇	semidirect
331. #463	C₂²×C₇	semidirect
332. #463	C₂²×C₇	semidirect
333. #463	C₂²×C₇	semidirect
334. #463	C₂²×C₇	semidirect
335. #462	C₂²×C₇	semidirect
336. #461	C₂²×C₇	semidirect
337. #461	C₂²×C₇	semidirect
338. #460	C₂²×C₇	semidirect
339. #459	C₂²×C₇	semidirect
340. #459	C₂²×C₇	semidirect
341. #424	C₂²×C₇	semidirect
342. #424	C₂²×C₇	semidirect
343. #423	C₂²×C₇	semidirect
344. C₂×C₄⋊C₈	C₂²×C₇	semidirect
345. #419	C₂²×C₇	semidirect
346. #418	C₂²×C₇	semidirect
347. #417	C₂²×C₇	semidirect
348. #417	C₂²×C₇	semidirect
349. #416	C₂²×C₇	semidirect
350. #416	C₂²×C₇	semidirect
351. C₂×#103	C₂²×C₇	semidirect
352. C₂×#102	C₂²×C₇	semidirect
417. H(5,𝔽₂)	C₇×D₄	semidirect
706. C₇	#60430	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₇×#577	2
C₂×C₇×#576	2
C₇×#3500	2
C₄×C₇×H(5,𝔽₂)	2
C₇×#3046	2
C₇×#3045	2
C₇×#3042	2
C₇×#3041	2
C₇×#3040	2
C₇×#3036	2
C₇×#3035	2
C₂×C₇×#463	2
C₇×#2906	2
C₇×#2898	2
C₇×#2897	2
#60430	7

Subgroups — C7×#60430 #13237646

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60430 #13237646